Problem 3

The following questions refer to the Red Brand Canners case discussed in class. Use the Excel outputs (file: RBC Question 3) to answer the following questions. THERE IS NO NEED TO RUN THE SOLVER.

Excel spreadsheet RBC refers to the following formulation.

Decision variables

AC= lbs. A in Canned

BC = lbs. B in Canned

AJ = lbs. A in Juice

BJ = lbs. B in Juice

AP = lbs. A in Paste

BP = lbs. B in paste

Max 24.7(AC + BC) + 19.8(AJ + BJ) + 22.2(AP + BP)

s.t.

AC + BC 14,400,000 (canned demand)

AJ + BJ 1, 000,000 (juice demand)

AP + BP 2, 000,000 (paste demand)

AC + AJ + AP 600,000 (A supply)

BC + BJ + BP 2,400,000 (B supply)

AC - 3BC > 0 (canned quality)

3AJ BJ > 0 (juice quality)

All variables nonnegative

Note: The objective function coefficients are expressed in cents/lb.

Using the Excel Output for RBC, what is the net profit obtained after netting out the cost of the tomatoes for the above formulation? Express it in $.

Review Meyers plan. Meyers thinks his policy will earn $144,000. Is this true? If not, how much will his plan earn after subtracting the cost of the crop?

Should the company go in for the additional purchase of up to 80,000 pounds of grade A tomatoes. How much should be bought?

Suppose an additional 100,000 pounds of grade B tomatoes is available. How much should RBC be willing to pay for this batch?

Is there a product(s) for which RBC should undertake an advertising campaign to increase its demand? How much should RBC be willing to pay for such a campaign?

Suppose that the price of juice increased by 30 cents per case. Will your recommendation change?

Suppose that RBC is forced to reduce the size of the product line in tomato-based products to 2. Would you need to rerun the Solver to tell which product should be dropped from the line?

Suppose an inspection of the crop reveals that there are three grades of tomatoes and not two as originally thought. A tomatoes average 9 points per pound, B tomatoes average 6 points per pound, and C tomatoes average 4 points per pound. There are 600,000 pounds of grade A quality, 1,600,000 pounds of grade B, quality and the remaining 800,000 pounds of C grade quality. Define

AC= lbs. A in Canned

BC = lbs. B in Canned

CC = lbs. C in canned

Write the quality constraint for the canned whole tomatoes. Whole tomatoes must have an average quality of 8 points per pound.